As in the previous section, the hopping parameter \(t\)  is real, \(\tau _i \sigma _j\)  are four-by-four matrices composed of Pauli matrices acting on the four degrees of freedom in the unit cell. Here, our basis consists of four fermionic operators \({c_{\mathbf {k}, a}, c_{\mathbf {k}, b}, c_{\mathbf {k}, c}, c_{\mathbf {k}, d}}\)  arranged as depicted in Fig. REF (a). Magnetic fourfold rotation exchanges the fermions in the unit cell counter-clockwise including a phase \(c_{\mathbf {k}, a} \rightarrow - c_{\mathbf {k}, c}\)  and a time-reversal operation implemented by complex conjugation.
This model can be adiabatically deformed to the chiral higher-order topological insulator of Ref. [1]}.
<FIGURE>